Basis Function Technique Research Articles

Using radial basis functions to approximate battery differential capacity and differential voltage

As part of the Department of Energy's Advanced Technology Development Program, lithium-ion cells of various sizes and chemistries are aged with periodic reference performance tests to ascertain degradation rates. The reference tests include a very slow discharge and charge based on a constant current equal to 1/25th of the rated capacity to elucidate the true electrochemical capacity of the cell. A differential analysis of these data helps to identify the individual kinetic and thermodynamic contributions of the anode and cathode. However, differential curves are very noisy, and previous smoothing methods included simple data reduction and moving averages. This paper introduces an alternative method of finding the differential voltage and differential capacity curves based on radial basis functions. The voltage profile is fit with a number of Gaussian curves, and the resulting model is differentiated. This approach also has the added advantage of assessing model uncertainty based on a bootstrap analysis. The radial basis function method was successfully applied to various lithium-ion chemistries tested under the Advanced Technology Development Program. The resulting differential capacity and differential voltage curves are generally smoother than the corresponding curves found by previous methods and also show little variance, indicating a good model fit. These results imply that the radial basis function technique is a more robust tool for assessing differential data.

An implicit upwinding volume element method based on meshless radial basis function techniques for modelling transport phenomena

AbstractThis work presents a control volume (CV) method for transient transport problems where the cell surface fluxes are reconstructed using local interpolation functions that besides interpolating the nodal values of the field variable, also satisfies the governing equation at some auxiliary points in the interpolation stencils. The interpolation function relies on a Hermitian radial basis function (HRBF) meshless collocation approach to find the solution of auxiliary local boundary/initial value problems, that are solved using the same time‐integration scheme adopted to update the global CV solution. By the use of interpolation functions that approximate the governing equation a form of analytical upwinding scheme is achieved, without the need of using predefined interpolation stencils according to the magnitude and direction of the local advective velocity. In this way, the interpolation formula retains the desired information about the advective velocity field allowing the use of centrally defined stencils even in the cases of advective dominant problems. This new CV approach is referred to as the CV‐HRBF method. Two time‐stepping formulations are considered: a full implicit approach and the weighted Crank–Nicholson one. The implicit upwinding scheme, intrinsic to the proposed CV‐HRBF, is tested by solving a travelling front problem at the Péclet number equal to 500, 1000 and infinity; with the latter corresponding to a shock front. Finally, the accuracy of the numerical method is validated against one‐ and three‐dimensional reactive transport problems characterized by smooth solutions. Copyright © 2009 John Wiley & Sons, Ltd.

A Control Volume Radial Basis Function Techniques for the Numerical Simulation of Saturated Flows in Semi-confined Aquifer

In this work, a Control Volume Radial Basis Function technique (CV-RBF) is adapted to solve ground water flow in the saturated zone of the semi-confined aquifer. The CV-RBF method differs from classical CV methods in the way that the flux at the cell surfaces is computed. A local RBF interpolation of the field variable is performed at the centres of the cell being integrated and its neighbours. This interpolation is then used to reconstruct the solution and its gradient in the integration points which support the flux computation. In addition, it is required that such interpolation satisfies the governing equation in a certain number of points placed around the cell centres. In this way, the local interpolations become equivalent to local boundary-value problems. The CV-RBF method is combined with a local remeshing technique in order to track the phreatic surface, where the gradients required to satisfy the kinematic condition are computed by the same local RBF interpolations used for the flux computation. The proposed numerical approach is validated in a series of three-dimensional groundwater flow problems where the operations of recharging and extracting water from a semi-confined aquifer are modelled.

Prediction of dynamical, nonlinear, and unstable process behavior

Process scheduling techniques consider the current load situation to allocate computing resources. Those techniques make approximations such as the average of communication, processing, and memory access to improve the process scheduling, although processes may present different behaviors during their whole execution. They may start with high communication requirements and later just processing. By discovering how processes behave over time, we believe it is possible to improve the resource allocation. This has motivated this paper which adopts chaos theory concepts and nonlinear prediction techniques in order to model and predict process behavior. Results confirm the radial basis function technique which presents good predictions and also low processing demands show what is essential in a real distributed environment.

Toward improved coal density estimation from geophysical logs

Density plays an important role in coal resource estimation and reconciliation, as well as in defining coal quality. Current practice employs direct density measurements on widely spaced core samples, rather than utilising abundant geophysical logging data. This is mostly due to the perception that the precision and accuracy of density estimation from geophysical logs is unsatisfactory. This paper demonstrates that the density wireline log, supported by other geophysical logs, provides a reliable direct measurement of in-situ coal density. We have produced a consistent and reliable correlation of geophysical log density with a laboratory-derived density to within an accuracy of ±3%. This is achieved through careful constraints such as compensating for lost pore spaces and moisture to bring the laboratory relative density closer to in-situ environmental conditions, matching the laboratory sample depths with geophysical logs, excluding thin, boundary, and stone-band samples from the dataset, and calibrating the geophysical density with laboratory testing data and other geophysical logs by linear regression or Radial Basis Function and Self-Organised Mapping techniques. In addition, we also illustrate that the improved geophysical log density can be used for coal quality estimation.

Improving Volume Element Methods by Meshless Radial Basis Function Techniques

Improving Volume Element Methods by Meshless Radial Basis Function Techniques

English

This paper presents with the performance of different loaded (e.g. inverted L, T, I and C-shaped antennas) and unloaded wire antennas as electromagnetic interference (EMI)sensors. To determine electromagnetic radiation from an electronic component, it isrequired to evaluate the field strength at a certain distance from it using the sensor. Themost common performance descriptor of a sensor is its antenna factor. Here, the methodof moments with pulse basis function and point-matching technique has been used to evaluatethe current distribution on the antenna surface, and hence, the antenna factor of different wireantennas. The same theory for unloaded antennas has been extended for different loaded-wireantennas. The loaded antennas in transmitting mode are widely used for low-frequencycommunication. However, while using these antennas as EMI sensors, the extra loading is likelyto introduce the reception of cross-polarised component of incident electric field. This paperhighlights the results of the initial investigation on the performance of these loaded antennasas EMI sensors in terms of the antenna factor for the desired and cross-polarised componentof incident electric field

Complex self-consistent field and multireference single- and double-excitation configuration interaction calculations for the Πg2 resonance state of N2−

Self-consistent field and multireference single- and double-excitation configuration interaction calculations employing the complex basis function technique are carried out for the (2)Pi(g) resonance state of the N(2) (-) molecule as well as several other anionic resonance states in the neighboring energy region. The results of calculations employing the same method for the (1)S (2s(2)) state of the He atom and the (1)Sigma(g) (+) (sigma(u) (2)) state of the H(2) molecule are found to be in good agreement with those of earlier work. The present theoretical treatment has succeeded for the first time in satisfying the rigorous criterion of the complex variational principle in computing the N(2) (-) resonance states, namely, a cusp in the plots of real versus imaginary components of the corresponding complex energies has been located at each internuclear distance. On this basis, it is found that the open-shell orbital in the lowest-energy adiabatic N(2) (-) resonance state of (2)Pi(g) symmetry changes its character from quite compact at large internuclear distance to relatively diffuse for r<2.3a(0). This is in contrast to all previous theoretical treatments of this system that have not rigorously satisfied the complex variational principle in their determination of this wave function.

Estimation of Equivalent Circuit of Loaded Trans-receive Antenna System and its Time Domain Studies

The time domain studies of different reduced-height loaded wire antennas (e.g., inverted L, T, I and C-shaped antennas) when used in trans-receive system is presented. Due to the reduced height of the loaded antennas, these antennas have found wide application as transmitting and receiving antenna/sensors for electromagnetic interference (EMI) measurements. However, while using these antennas in trans-receive system for wideband application, the time domain characterization of both the transmit and receive antenna is required and investigation on this has not yet been performed. This paper presents the results of the initial investigation on the time-domain performance of these loaded trans-receive systems. An optimized transmit antenna generator waveform is used to maximize receive antenna voltage amplitude (with bounded input energy), as presented in the recent literature. The frequency domain Method of Moments with Pulse basis function and Point-matching technique has been used to evaluate the current distribution on the antenna surface and hence the radiated electric field at the position of the receiving antenna. The same technique has been extended for receiving wire antenna to evaluate the Complex Antenna Factor (CAF) of these antennas. The CAF versus frequency data has been used to evaluate the input and output voltage waveform of the trans-receive system. The results have been verified with theoretical and experimental data available in reported works.

General solutions and fundamental solutions of varied orders to the vibrational thin, the Berger, and the Winkler plates

In this note, we derive the general and the fundamental solutions of varied orders of vibrational thin plate, Berger plate, and Winkler plate. These solutions are of important use in the multiple reciprocity BEM, dual reciprocity BEM, boundary particle method, boundary knot method, and a variety of radial basis function techniques.

Level Density in the Complex Scaling Method

It is shown that the continuum level density (CLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states, resonances and continuum states are obtained in terms of $L^2$ basis functions. In this method, the extended completeness relation is applied to the calculation of the Green functions, and the continuum-state part is approximately expressed in terms of discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss how the scattering phase shifts can inversely be calculated from the discretized CLD using a basis function technique in the CSM.

LOADED WIRE ANTENNA AS EMI SENSOR

This paper describes the performance of different loaded wire antennas (e.g., inverted L, T, I and C-shaped antennas) as electromagnetic interference (EMI) sensors. Loaded wire antennas in transmitting mode are widely used for low frequency communication. However, while using these antennas as EMI sensors, the extra loading is likely to introduce the reception of cross-polarized component of incident electric field and investigation on this has not yet been performed. This paper highlights the results of the initial investigation on the performance of these loaded antennas as EMI sensors in terms of the Antenna Factor for the desired and cross-polarized component of incident electric field. The Method of Moments with Pulse basis function and Point-matching technique has been used to evaluate the current distribution on the antenna surface and hence the Antenna Factor.

Agricultural water use estimation using geospatial modeling and a geographic information system*1

Fresh water resources in the world are limited and, often, disputes occur on how to share them. In many regions, agricultural water use is significant but poorly documented. In order to contribute to solutions for water disputes involving such regions, methodologies need to be developed for regional water use estimation. In this paper we present a case study of Georgia (USA) which is locked in a water dispute with its neighboring states—Alabama and Florida. Agricultural water use in Georgia was essentially unknown because of no reporting requirement. Using a geographic information system and geospatial techniques, the depths of irrigation for cotton, peanut, and maize are estimated for the Flint, Central, and Coastal water zones of Georgia for 2000–2002. The geospatial techniques included the Inverse Distance Weighting, Global Polynomial, Local Polynomial, Radial Basis Function, Ordinary Kriging, and Universal Kriging. The volume of irrigation for these crops was estimated for 2000 and 2001. On the basis of root mean squared error, the Radial Basis Function technique was found to be the most successful one, followed by the Local Polynomial technique. The study of variograms revealed that the depth of irrigation at a site was influenced by its neighboring sites within a radius of about 40 km in the case of cotton, and within about 70 km in the case of peanut. No such influence could be detected for maize. The total volume of irrigation was highest for the Flint zone (564.2 Mm3), followed by the Central zone (291.9 Mm3) and the Coastal zone (94.1 Mm3) for 2000. For 2001, the irrigation volume declined by 40% for the Flint zone, 32% for the Central zone, and 16% for the Coastal zone. The estimates presented in this study can be improved by including more representative sampling sites if possible, by studying the patterns of irrigated lands in Georgia, and by using satellite data for estimating irrigated area for individual crops.

Agricultural water use estimation using geospatial modeling and a geographic information system

Fresh water resources in the world are limited and, often, disputes occur on how to share them. In many regions, agricultural water use is significant but poorly documented. In order to contribute to solutions for water disputes involving such regions, methodologies need to be developed for regional water use estimation. In this paper we present a case study of Georgia (USA) which is locked in a water dispute with its neighboring states—Alabama and Florida. Agricultural water use in Georgia was essentially unknown because of no reporting requirement. Using a geographic information system and geospatial techniques, the depths of irrigation for cotton, peanut, and maize are estimated for the Flint, Central, and Coastal water zones of Georgia for 2000–2002. The geospatial techniques included the Inverse Distance Weighting, Global Polynomial, Local Polynomial, Radial Basis Function, Ordinary Kriging, and Universal Kriging. The volume of irrigation for these crops was estimated for 2000 and 2001. On the basis of root mean squared error, the Radial Basis Function technique was found to be the most successful one, followed by the Local Polynomial technique. The study of variograms revealed that the depth of irrigation at a site was influenced by its neighboring sites within a radius of about 40 km in the case of cotton, and within about 70 km in the case of peanut. No such influence could be detected for maize. The total volume of irrigation was highest for the Flint zone (564.2 Mm 3), followed by the Central zone (291.9 Mm 3) and the Coastal zone (94.1 Mm 3) for 2000. For 2001, the irrigation volume declined by 40% for the Flint zone, 32% for the Central zone, and 16% for the Coastal zone. The estimates presented in this study can be improved by including more representative sampling sites if possible, by studying the patterns of irrigated lands in Georgia, and by using satellite data for estimating irrigated area for individual crops.

Path integral variational methods for strongly correlated systems.

We introduce a new approach to highly correlated systems which generalizes the Fermi Hypernetted Chain and Correlated Basis Function techniques. While the latter approaches can only be applied to systems for which a nonrelativistic wave function can be defined, the new approach is based on the variation of a trial hamiltonian within a path integral framework and thus can also be applied to relativistic and field theoretical problems. We derive a diagrammatic scheme for the new approach and show how a particular choice of the trial hamiltonian corresponds exactly to the use of a Jastrow correlated ansatz for the wave function in the Fermi Hypernetted Chain approach. We show how our new approach can be used to find upper bounds to ground state energies in systems which the FHNC cannot handle, including those described by an energy-dependent effective hamiltonian. We demonstrate our approach by applying it to a quantum field theoretical system of interacting pions and nucleons.

Basis function-based adaptive critic learning and its learning parameters selection

An adaptive critic learning (ACL) structure consists of two modules: the action and the critic ones. Learning occurs in both modules. The critic module learns to evaluate the system status. It transforms occasionally occurred failure signals into useful evaluation information. Utilizing such information, the action module can learn the control technique. In this paper, we investigate the technique of using basis functions (BFs) in ACL. One difficulty in the scheme is on selection of learning parameters. Without a guideline, the best set of learning parameters must be obtained from a large number of test simulations. This study investigated the effects of parameters through analysis and verified the analytical results by simulations. In addition to the problem of parameter selection, effects of measurement errors on the CMAC-based (one basis function technique) ACL have been also examined and reported.

Extension of the Rees basis function technique to simulate nonstationary transport

Shrinking device geometries have caused considerable interest in accurately modeling nonstationary in semiconductors using computationally efficient techniques. In this paper we describe an extension to a basis function technique first proposed by Rees (1973), to model nonstationary effects of electron in semiconductors. While the central focus of this paper is to demonstrate and analyze a novel technique to compute a good basis set (based on the local-effect and flux operations first described by Rees), the Rees technique itself is described in some detail here to serve as the foundation for subsequent arguments. Basis functions computed in this way are not restricted for use in the Rees technique alone-they are also useful in any approach that solves the semi-classical Boltzmann equation (BTE) spectrally. However, use of such functions in the Rees spectral technique allows the minimum simulation time-step of the precomputed transport matrices to be significantly reduced. Simulation results are presented to demonstrate this improvement in a limited field range. >

Optimal reconstruction of missing-pixel images

A basis-function technique for reconstructing images with missing pixels is described. This technique yields optimal reconstructed image smoothness in that each basis-function width is maximized consistent with an acceptable level of computational effort.

On the training of radial basis function classifiers

An approach for the implementation of the Radial Basis Function (RBF) technique is presented and applied to a network of the appropriate architecture. The paper explores a methodology for selecting kernel function parameters and the extent to which the number of RBF nodes can be reduced without significantly affecting the overall training error. These objectives are accomplished through algorithms that shall be described in detail. Emphasis is also placed on the problems faced by a technique that has been proved superior to the more traditional training algorithms, particularly in terms of processing speed and solvability of nonlinear patterns. Solutions are consequently proposed in view of making RBF a more efficient method for interpolation and classification purposes.

An algebraic variational approach to the calculation of total cross sections for one- and two-photon ionization

We outline a method for computing total cross sections for one- and two-photon ionization from a stationary principle. The method is based on a generalization of the complex Kohn variational method, recently developed for studying electron-neutral atom/molecule collisions. It also has features common to complex basis function techniques. The method is illustrated by application to atomic hydrogen in its ground and various excited states.